Dodger General Manager Ned Colletti and President and part Dodger Owner Stan Casten held a press conference at Dodger Stadium to formally announce the $215 million contract for pitcher Clayton Kershaw. Los Angeles, CA January 15, 2014.(John McCoy/Los Angeles Daily News)

If you’ve ever seen Clayton Kershaw play ping-pong, you figure he might have been sweating this week — not because there was a deadline Friday for teams to sign arbitration-eligible players before exchanging salary figures, but because of how Kershaw celebrated signing his seven-year, $215 million contract.

He played ping-pong and grilled burgers with his friends and family at his home near Dallas, Texas.

The Dodgers might be sweating over a pitcher but not Kershaw, whose contract became official Friday. Negotiations began in March 2013, and team president Stan Kasten said the first contract proposal “wasn’t all that far away from where we wound up.”

“There was never any urgency, a feeling of get-this-done-now-or-else, from either side,” Kasten said. “If it had taken until next year, I wouldn’t have been surprised if we signed him then also because the relationship has been great.”

Talks slowed during the season and resumed again this winter.

“We’d have a conversation and we’d get back to the other side a week or two later,” Kasten said.

Dodgers general manager Ned Colletti said it was important not to press hard with negotiations in-season. When talks turned toward a larger deal last summer — reported at 10 years and close to $300 million — a long pause followed. Kershaw seemed to appreciate the Dodgers’ laid-back approach.

“I think there’s never been a sense of urgency, with the fact that I was going to be in L.A. this next year regardless,” he said. “Ned and Stan got everything done at the beginning of the offseason, with free agency and everything they were trying to do. It gave us a chance to focus on it for a solid week or two.”

Because Kershaw is Kershaw and because his $215 million contract is the largest ever given a pitcher, he became a priority once the Dodgers had signed their top free-agent targets — Alexander Guerrero, Dan Haren, Juan Uribe, Brian Wilson, J.P. Howell, Jamey Wright and Chris Perez.

Now comes perhaps their biggest challenge of the offseason.

Masahiro Tanaka is the consensus best pitcher on the market. Colletti said he’s been talking to Tanaka’s agent “not yesterday, but every day this week.” Tanaka must sign with a major-league team by next Friday or return to his Japanese club, the Rakuten Golden Eagles.

Just last year, Colletti went through the posting process with Korean left-hander Hyun-Jin Ryu. That contract wasn’t signed and delivered to MLB until literally the final minute before the deadline.

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“I don’t know if this will go down to the last minute like it did with Ryu,” Colletti said. “Most of that’s under their control. We’ll play it for as long as we can play it until we know that we’re out.”

That might be the strongest statement of interest yet by a general manager toward Tanaka, and it’s a sign the Dodgers are anything but out. The Kyodo News reported Tanaka hasn’t narrowed his choices since meeting with representatives from multiple clubs last week in Los Angeles. The Chicago White Sox, Chicago Cubs and New York Yankees were among the teams who reportedly met with the pitcher and his agent; the Angels reportedly did not.

Coincidentally, Kershaw and Tanaka share an agent, Casey Close. Kershaw said he hasn’t personally attempted to sell Tanaka on the merits of playing in Los Angeles.

“From what I hear, he seems like a great pitcher,” Kershaw said of Tanaka. “If he’s a great pitcher, it definitely can never hurt.”

If Kershaw hadn’t re-signed by 10 a.m. Friday, he and the Dodgers would have had to file their respective one-year salary proposals. If they still could not strike an agreement, an arbitration panel would choose either Kershaw’s proposal or the Dodgers’ proposal in February.

Closer Kenley Jansen and catcher A.J. Ellis were the Dodgers’ other arbitration-eligible players. Since neither player signed before the deadline, they exchanged proposals with the Dodgers on Friday.

Jansen has filed for $5.05 million and the Dodgers $3.5 million. Jansen earned saves in 28 of his 32 opportunities in 2014 and 25 of 32 chances in 2013 and led the team in saves both years. His career average of 14 strikeouts per nine innings is among the best in the major leagues, and his 1.88 earned-run average was the lowest among Dodgers relievers with at least 20 appearances.

The 26-year-old made $512,000 last year and is arbitration-eligible for the first time.

Ellis, 32, batted .238 with 10 home runs and 52 RBIs in his second season as the Dodgers’ starting catcher. He’s also a clubhouse leader whose catchers’ ERA of 3.06 was the lowest in the major leagues in 2013. Ellis made $2 million last year, his first year of arbitration eligibility. He’s requested $4.6 million and the Dodgers have offered $3 million.

The Angels re-signed closer Ernesto Frieri and reliever Fernando Salas before Friday’s deadline for $3.8 million and $870,000 respectively. Third baseman David Freese and reliever Kevin Jepsen each filed salary proposals.

According to multiple reports, Jepsen is seeking $1.625 million and the Angels countered with $1.3 million. Freese and the Angels are a bit farther apart. He’s seeking $6 million and the Angels are offering $4.1 million.